A placekicker kicks a football at an

angle of 60°. At what angle will the
football hit the ground.

-60 degrees.

Due to conservation of energy, the speed remains the same at kickoff and receipt. The horizontal V component remains the same and the vertical V component only changes sign.

To determine the angle at which the football hits the ground, we need to consider the motion of the football in two separate directions: horizontal and vertical.

Given that the initial angle of the kick is 60°, we can split the initial velocity of the football into its horizontal and vertical components. The horizontal component remains constant throughout the time of flight, while the vertical component is affected by gravity.

Let's assume the initial velocity of the football is V.

The vertical component of the initial velocity (V_y) can be calculated using the sine function:

V_y = V * sin(60°)

The horizontal component of the initial velocity (V_x) can be calculated using the cosine function:

V_x = V * cos(60°)

When the football hits the ground, the vertical displacement would be equal to zero. We can use the equation of motion to find the time of flight (t):

0 = V_y * t - 0.5 * g * t^2

Where g is the acceleration due to gravity.

Since the football is going upwards before reaching the peak, the vertical component of velocity will be negative. So we can rewrite the above equation as:

0 = -V * sin(60°) * t - 0.5 * g * t^2

Now we can solve this equation for time (t).

Once we have the time of flight, we can find the horizontal displacement (d) using the equation:

d = V_x * t

Now, the angle at which the ball hits the ground can be determined using the tangent function:

tan(θ) = V_y / V_x

Rearranging the equation to solve for θ, we get:

θ = tan^(-1) (V_y / V_x)

Plugging in the values we previously obtained:

θ = tan^(-1) ((V * sin(60°)) / (V * cos(60°)))

θ = tan^(-1) (tan(60°))

θ = 60°

Therefore, the football will hit the ground at an angle of 60°.

To determine the angle at which the football will hit the ground, we need to understand the basic principles of projectile motion.

In this scenario, the placekicker is kicking a football at an angle of 60°. We can break down the motion of the football into two components: horizontal and vertical. The horizontal component determines the distance the football travels, while the vertical component determines its height and the time it takes to reach the ground.

Because the angle of projection is 60°, we can split it into two equal angles of 30°. The vertical component can be determined using the sine function, while the horizontal component can be determined using the cosine function.

Let's say the magnitude of the initial velocity (speed) of the football is v. The initial velocity in the horizontal direction (v_x) can be calculated using the equation:

v_x = v * cos(θ),

where θ is the angle of projection (60°).

Similarly, the initial velocity in the vertical direction (v_y) can be calculated using the equation:

v_y = v * sin(θ).

Now, as the football is subject to gravitational acceleration (g) in the vertical direction, we need to consider the time it takes for the football to hit the ground. The time of flight (T) can be calculated using the equation:

T = (2 * v_y) / g.

Finally, to determine the angle at which the football hits the ground (α), we can use the equation:

tan(α) = v_y / v_x.

By substituting the values of v_x and v_y, we can solve for α:

tan(α) = (v * sin(θ)) / (v * cos(θ)).

Simplifying the equation:

tan(α) = tan(θ).

Since the tangent function is periodic, we can conclude that α = θ.

Therefore, in this case, the football will hit the ground at an angle of 60°.